RiverVortexTest

From Gerris

Testing the River version of Gerris. In particular interested in the possibility of tidal turbine
like simulations in support of Tim Divett's thesis.

The basic issue is that we note in both the Linear Free Surface and Nonlinear Free Surface versions
of Gerris that vortices generated from wakes caused by localised regions of high bottom friction
(mimicing the presence of a turbine, say) can sometimes become unstable, i.e., the vortex continues
to spin up as it moves downstream leading to (presumably) unphysical magnitudes of flow and fluid
height. In the linear free surface version, such vortices persist and can be seen moving with the
background flow. In the nonlinear free surface version, these vortices become tighter and more
intense, and eventually grind the simulation to a halt via excessive magnitudes of flow and amplitude.

This issue is also relevant to a whole series of linear free surface tidal simulations around headlands
and bays around New Zealand. In these simulations an increase in spatial resolution reveals the
generation of many eddies that appear to be shed in a physical way via interactions with the
coastline. As above, these eddies persist in the background tidal flow. They do not appear to
be unstable (ie the runs keep going), but the question remains about the fidelity and actuality
of these eddies (and to test this we need more field observations, and perhaps some more thought
about the model).

Both models have been tested against the cases present by Signell and Geyer (1991) and both seem
to do a good job of reproducing many of the features seen. Thus the underlying schemes seem to be
correct, at least for the scales of interest in these tests.

Perhaps it's not surprising that these features arise. After all the models in question here are
solving shallow water variants of reality, so that the likely possibility of 3D processes in the
water column influencing the vortex behaviour is absent. For the shallow water the only explicit
damping is via a bottom friction term, and the only implicit damping is through truncation terms
in the advection scheme; these may be missing important physics that allow for a more complete
representation of the vortex behaviour.

So, here show some examples of the unstable vortex behaviour in the River code. This can perhaps
lead to a better understanding of the limitations of the shallow water models, and how far we
should be pushing them to look at the (presumably) complex tidal interactions with coastline
and in-situ structures.